In mathematics, a highly abundant number is a certain kind of natural number. Formally, a natural number n is called highly abundant iff for all m < n,

σ(n) > σ(m)

where σ denotes the divisor function. The first few highly abundant numbers are 1, 2, 3, 4, 6, 8, 10, 12, 16, 18, 20, 24, 30, 36, 42, 48, 60, ... .

Also see

• Colossally abundant number
• Superabundant number
• Abundant number
• Deficient number